Optimizing Security Patrolling Strategies A Cross-Domain Review of Mathematical Models and Applications

This book presents a comprehensive examination of crime patrolling problems across various domains, including robotics, security, and law enforcement, with a focus on the mathematical models used to optimize patrolling strategies. Patrolling is a critical crime prevention and deterrence strategy, requiring the effective allocation of resources to address evolving security challenges.  In addition, patrolling is one of the most effective and widely adopted crime prevention and deterrence strategies worldwide. It is integral to security agencies such as police and military forces across various domains, including land, air, and maritime areas. As such, effective patrolling requires the coordination of manpower, technological resources, and policies to address evolving security challenges.  The authors review recent research on robotic patrolling, multirobot systems, and police patrolling and also explore advances in modeling, optimization, and practical applications.  In addition, the author’s analysis categorizes studies by core modeling themes, such as Game Theory, Mathematical Optimization, and Stochastic methods, and highlights the secondary modeling themes that frequently complement the primary approaches.  Each study is categorized by fields including, but not limited to domain, patrolling focus, area representation, and solution methodology to facilitate cross-comparison. The book identifies gaps in current research, particularly the lack of a holistic examination of patrolling from robotic, autonomous, human, and hybrid perspectives, and proposes future directions for research in this evolving field.

Introduction.- Review Methodology.- Analysis of the Literature.- Future Research Directions.- Concluding Discussion. References.

Yusuf Ihsan Tokel is a Ph.D. candidate in the Department of Industrial and Systems Engineering at the University at Buffalo. His research interests focus on data-driven decision-making, game theory, and combinatorial optimization. He is interested in a niche area of game theory known as signaling theory, having already published on the topic.  Additionally, he is conducting a data-driven study to analyze the smuggling activities internationally and understand immigration trends to the U.S. from countries outside of South and Central America, aiming to improve the accuracy of models in this under-studied domain. As part of his dissertation, he is developing mathematical optimization models to optimize resource allocation in dynamic security environments, while also using game-theoretic approaches to analyze strategic interactions with adaptive adversaries across various security contexts.

Jun Zhuang, Ph.D., is the Associate Dean for Research in the School of Engineering and Applied Sciences and the Morton C. Frank Professor in the Department of Industrial and Systems Engineering  at the University at Buffalo, which is part of the State University of New York. Dr. Zhuang obtained his Ph.D. in Industrial Engineering from the University of Wisconsin-Madison in 2008. His primary research objective is to integrate operations research, big data analytics, game theory, and decision analysis to enhance mitigation, preparedness, response, and recovery in the face of natural and man-made disasters. Additionally, he explores other domains such as healthcare, sports, transportation, supply chain management, sustainability, and architecture. Dr. Zhuang has acted as a principal investigator for more than 40 research grants funded by various organizations, including the U.S. National Science Foundation (NSF), the U.S. Department of Homeland Security (DHS), the U.S. Department of Energy (DOE), the U.S. Air Force Office of Scientific Research (AFOSR), and the National Fire Protection Association (NFPA).